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1, 3, 6, 9, 15, 18, 28, 30, 36, 45, 66, 60, 91, 84, 90, 100, 153, 126, 190, 150, 168, 198, 276, 210, 225, 273, 270, 280, 435, 315, 496, 360, 396, 459, 420, 441, 703, 570, 546, 540, 861, 588, 946, 660, 675, 828, 1128, 756, 784, 825, 918, 910, 1431, 945, 990, 1008, 1140, 1305, 1770
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OFFSET
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1,2
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COMMENTS
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When n squares are arranged in a rectangular grid which is as nearly square as possible, a(n) represents the count of rectangles in the grid. The whole grid itself must be a rectangle too.
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LINKS
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EXAMPLE
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For n=10, the grid as nearly square as possible is 2*5. Thus a(10)=3*15=45 is the number of rectangles in this grid.
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MATHEMATICA
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Table[(# (# + 1)/2) &[
First[Select[Divisors[n], # >= Sqrt[n] &]]] (# (# + 1)/2) &[
Last[Select[Divisors[n], # <= Sqrt[n] &]]], {n, 80}]
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PROG
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(PARI) t(n) = n*(n+1)/2; \\ A000217
largdiv(n) = if(n<2, 1, my(d=divisors(n)); d[(length(d)+1)\2]); \\ A033676
a(n) = my(d=largdiv(n)); t(d)*t(n/d); \\ Michel Marcus, Jul 18 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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